Thermodynamic reassessment of the Au–Dy system supported by first-principles calculations

Based on the available experimental phase equilibria and thermodynamic data and enthalpies of formation computed via first-principles calculations, thermodynamic reassessment of the Au–Dy system was carried out by means of the CALPHAD method. The enthalpies of formation at 0 K for AuDy₂, αAuDy, βAuDy, Au₂Dy, Au₃Dy, Au₅₁Dy₁₄ and Au₆Dy were computed via first-principles calculations to supply the necessary thermodynamic data for the modeling in order to obtain the thermodynamic parameters with sound physical meaning. The solution phases, i.e. liquid, (Au), (αDy) and (βDy), were described by the substitutional solution model, and all the intermetallic compounds in the Au–Dy system were treated as stoichiometric phases. A set of self-consistent thermodynamic parameters for the Au–Dy system was finally obtained. The calculated phase diagram and thermodynamic properties agree reasonably with the literature experimental data and the present first-principles calculations.     

Liquid phase separation,solidification and phase transformations of Gd–Ti and Gd–Ti–Al–Cu alloys

Phase equilibria of the quaternary Gd–Ti–Al–Cu system have been studied with particular respect to solidification and phase separation phenomena in metallic glasses. Along the section Gd_55−xTi_xAl₂₅Cu₂₀ the primary solidifying phase changes from Gd₂CuAl (x=0) toward α-Ti (x≥10) with rising Ti-fraction x. This is accompanied by an upturn of the liquidus temperature from T_L=745 °C to T_L>1100 °C. The miscibility gap predicted from thermodynamic calculations for Gd_55−xTi_xAl₂₅Cu₂₀ melts at intermediate Ti-fractions was not verified experimentally. Unlike binary Gd–Ti melts, levitated Gd–Ti–Al–Cu droplets do not exhibit liquid phase separation features after quenching from different holding temperatures, even at high melt undercooling up to 200 K prior to solidification.     

Asymmetric mixing behavior and stability of the predicted phases in the W–Cu system

The W–Cu system is strongly immiscible both in the solid and liquid phases. By combining cluster expansion method with first-principles calculations, present calculations clearly show that there is asymmetric mixing behavior for both FCC and HCP lattices in the W–Cu system. This asymmetric behavior affects the cohesion of the immiscible W–Cu system and is confirmed by Cu/W multilayers ion-bean mixing experiment and Compton scattering observation in the literature. Moreover, the predicted energetically metastable phases of L1₂ CuW₃ and D0₁₉ CuW₃ are confirmed to be mechanically and vibrationally stable at zero temperature. The further calculated Helmholtz free energy of formation as a function of temperature from lattice dynamics shows that the L1₂ phase is more stable than D0₁₉ phase when temperature is lower than 350 K.     

Thermodynamic assessment of the cesium–oxygen system by coupling density functional theory and CALPHAD approaches

The thermodynamic properties of cesium oxides were calculated by combining ab initio calculations at 0 K and a quasi-harmonic statistical thermodynamic model to determine the temperature dependency of the thermodynamic properties. In a second approach, the CALPHAD method was used to derive a model describing the Gibbs energy for all the cesium oxide compounds and the liquid phase of the cesium–oxygen system. For this approach, available experimental data in the literature was reviewed and it was concluded that only experimental thermodynamic data for Cs₂O are reliable. All these data together with the thermodynamic data calculated by combining ab initio and the statistical model were used to assess the Gibbs energy of all the phases of the cesium–oxygen system. A consistent thermodynamic model was obtained. The variation of the relative stability of the different oxides is discussed using structural and bond data for the oxides investigated by ab initio calculations. This work suggests that the melting point for Cs₂O₂ reported in the literature (863 K) is probably overestimated and should be re-measured.     

Thermodynamic calculation of the T0 curve and metastable phase diagrams of the Ti–M (M = Mo,V, Nb,Cr, Al) binary systems

Based on the experimental data available in the literature, the β-α′/α′′⬠ martensitic transformation and athermal ω formation of the Ti–M (M = Mo, V, Nb, Cr, Al) binary systems at low temperature are thermodynamically described. According to β-α′/α′′⬠ martensitic transformation and metastable ω phase formation temperatures, thermodynamic parameters of these systems are assessed by means of the CALPHAD (CALculation Phase Diagram) approach supported by first-principles calculations. In addition to the metastable ω phase, only solution phases, i.e. liquid, α(hcp), β(bcc) or γ(fcc) are included and their thermodynamic parameters are adopted in the literature or revised in this work. The metastable phase diagrams of the Ti–M (M = Mo, V, Nb, Cr, Al) systems with T₀(β/α) and T₀(β/ω) curves are calculated using the obtained parameters. Comparisons between the calculated results and experimental data reported in the literature show that almost all the reliable experimental information can be satisfactorily accounted for by the present modeling.     

Thermodynamic modeling of Fe–Ti–Bi system assisted with key experiments

Phase equilibria of Fe–Ti–Bi ternary system have been studied in this work. Firstly, by using alloy sampling, the isothermal section of Fe–Ti–Bi ternary system at 773 K was determined, where the existence of a ternary phase Bi₂FeTi₄ was confirmed. Meanwhile, formation enthalpies of the intermediate phases BiTi₂, Bi₉Ti₈ and Bi₂FeTi₄, were obtained with first-principles calculations. Based on experimental data of phase equilibria and thermodynamic properties in literatures along with the calculated formation enthalpies in this work, thermodynamic modeling of Ti–Bi binary system and Fe–Ti–Bi ternary system were carried out with the CALPHAD approach. A set of self-consistent thermodynamic parameters to describe the Gibbs energy for various phases in Fe–Ti–Bi ternary system was finally obtained, with which solidification processes of two typical Fe–Ti–Bi alloys could be reasonably explained.     

Phase equilibria in Fe–Sn–Ti ternary system at 1073 K and 1273 K

Phase equilibria in the Fe–Sn–Ti ternary system at 1073 and 1273 K were experimentally investigated through alloy sampling approach facilitated with electron probe micro-analyzer and X-ray diffraction. Two ternary compounds TiFe₂Sn and Ti₂FeSn were detected. Ten 3-phase equilibria at 1073 K, including β(Ti)+Ti₃Sn+FeTi, Ti₃Sn+FeTi+Ti₅Sn₃, FeTi+Ti₅Sn₃+Ti₂FeSn, Ti₂FeSn+Fe₂Ti+TiFe₂Sn, Ti₂FeSn+Ti₅Sn₃+Ti₆Sn₅, FeTi+Fe₂Ti+Ti₂FeSn, Ti₂FeSn+Ti₆Sn₅+TiFe₂Sn, TiFe₂Sn+Ti₆Sn₅+Liquid, TiFe₂Sn+Fe₅Sn₃+Liquid and α(Fe)+Fe₂Ti+TiFe₂Sn, and seven 3-phase equilibria including β(Ti)+Ti₃Sn+FeTi, Ti₃Sn+FeTi+Ti₅Sn₃, Ti₃Sn+Ti₂Sn+Ti₅Sn₃, FeTi+Fe₂Ti+Ti₅Sn₃, Fe₂Ti+Ti₂FeSn+Ti₅Sn₃, Ti₂FeSn+Fe₂Ti+TiFe₂Sn and Ti₂FeSn+Ti₆Sn₅+TiFe₂Sn at 1273 K were experimentally confirmed. At 1073 K, the homogeneity ranges of Ti₂FeSn were 45.5–51.4 at% Ti and 24–27.7 at.% Sn while TiFe₂Sn exhibited a large homogeneity range of 46.9–66.4 at% Fe and 22.7–26.4 at% Sn, the solubility of Sn in Fe₂Ti,Fe in Ti₅Sn₃, Ti in Fe₅Sn₃ and Fe in Ti₆Sn₅ can be up to 4.6 at.%, 10.2 at%, 3.7 at% and 21 at%, respectively, while at 1273 K, Solubility of Sn in Fe₂Ti considerably increased to 10.8 at%, Fe in Ti₅Sn₃ changes little. According to the measured phase relations, an invariant reaction was further deduced, which was Fe₂Ti+Ti₅Sn₃↔FeTi+Ti₂FeSn occurring between 1073 K and 1123 K.     

Thermodynamic reassessment of the novel solid-state thermal energy storage materials: Ternary polyalcohol and amine system pentaglycerine-tris(hydroxymethyl)-amino-methane-neopentylglycol (PG-TRIS-NPG)

Organic polyalcohol and amine globular molecular crystals such as PG, TRIS, and NPG are considered as the most promising potential candidates for solid-state thermal energy storage in the orientationally disordered high temperature phases. In this study, we first propose a new PG-TRIS-NPG phase diagram based on experimental data of the three sub-binary systems NPG-PG, PG-TRIS, and NPG-TRIS with CALPHAD methodology. The NPG-PG binary phase diagram was optimized using sub-regular models that showed complete miscibility in the entire compositional range of high temperature γ′ (FCC) phase region, and an invariant equilibrium point at 299.5 K. The NPG-TRIS binary system was also calculated using sub-regular model, from sub-ambient to well above the melting temperatures, and determined three invariant equilibria at 311.1 K, 391.8 K, and 410.6 K, respectively. These calculated binary phase diagrams are in good agreement with the experimental data. The PG-TRIS-NPG ternary system has also been calculated and qualitatively analyzed using the CALPHAD method and Thermo-Calc software. A set of self-consistent thermodynamic parameters formulating the Gibbs energies of various phase in the PG-TIRS-NPG ternary system are obtained in the present work. Thermodynamic properties such as several isotherms, isopleths, and liquidus projections are calculated by using present datasets as shown in this work in which the solid ternary compound (TRIS_0.5NPG_0.5)_XPG_1−X (0.1≤x≤0.9), (TRIS_0.5PG_0.5)_XNPG_1−X (0.1≤x≤0.9), and (PG_0.5NPG_0.5)_XTRIS_1−X (0.1≤x≤0.9) with various solid-solid phase transitions at different temperatures could apply to applications in the solid-state thermal energy storage.     

Calphad-type assessment of the Sb–Sn–Zn ternary system

The ternary Sb–Sn–Zn phase diagram was investigated experimentally by scanning electron microscopy (SEM) and differential thermal analysis (DTA) of long-term annealed samples. The overall composition of each sample was measured by energy-dispersive X-ray spectroscopy (EDX). The experimental results, together with additional available literature data, were used to perform a CALPHAD-type thermodynamic assessment of this ternary system. Two calculated isothermal sections (250 and 350 °C), an isopleth (x(Sn)=17.57%) and the Zn activity in liquid ternary Sb–Sn–Zn alloys at 550 °C for the composition ratio Sn/Sb=1/3 and at 650 °C for the ratio Sn/Sb=9 are presented with experimental points superimposed. The liquidus projection for the ternary Sb–Sn–Zn system is also presented. The agreement between calculated and experimental results is reasonable.     

Experimental investigation and thermodynamic calculation of the Fe–Si–Sn system

Phase equilibrium of the Fe–Si–Sn ternary system was investigated using equilibrated alloys. The samples were characterized by means of scanning electron microscopy equipped with energy dispersive X–ray spectrometry and X–ray diffraction. Isothermal sections of the Fe–Si–Sn system at 700 °C and 890 °C each consists of 5 three–phase regions. No ternary compound was found at those two temperatures. The solubility of Sn in the Fe–Si binary phases and the solubility of Si in the Fe–Sn binary phases is limited. Furthermore, thermodynamic extrapolation of the Fe–Si–Sn system was carried out. Calculated solidification path and phase relationship agreed well with experimental results.     

Thermodynamic study of the cerium–cadmium system

Cadmium vapor pressures were determined over Ce–Cd samples by an isopiestic method. The measurements were carried out in the temperature range from 690 to 1080 K and over a composition range of 48–85 at% Cd. From the vapor pressures thermodynamic activities of Cd were derived for all samples at their respective sample temperatures, and partial molar enthalpies of Cd were obtained from the temperature dependence of the activities. With these partial molar enthalpies the Cd activities were converted to a common temperature of 823 K. By means of a Gibbs–Duhem integration Ce activities were calculated, using a corresponding literature value for the two-phase field (CeCd₁₁+L) as integration constant. Finally integral Gibbs energies were calculated for the composition range 48–100 at% Cd with a minimum value of −37 kJ g-atom⁻¹ at 823 K in the phase CeCd. Phase boundaries of the intermetallic compounds CeCd, CeCd₂, Ce₁₃Cd₅₈, and CeCd₁₁ were estimated from the vapor pressure measurements and from SEM analyses.